LOW TEMPERATURE ACOUSTIC PROPERTIES OF SILICA AEROGELS

HAL Id: jpa-00227179

https://hal.archives-ouvertes.fr/jpa-00227179

Submitted on 1 Jan 1987

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

LOW TEMPERATURE ACOUSTIC PROPERTIES OF SILICA AEROGELS

J. Bon, E. Bonjour, R. Calemczuk, B. Salce

To cite this version:

J. Bon, E. Bonjour, R. Calemczuk, B. Salce. LOW TEMPERATURE ACOUSTIC PROPER- TIES OF SILICA AEROGELS. Journal de Physique Colloques, 1987, 48 (C8), pp.C8-483-C8-488.

�10.1051/jphyscol:1987875�. �jpa-00227179�

JOURNAL DE PHYSIQUE

C o l l o q u e C8, s u p p l e m e n t a u n 0 1 2 , Tome 48, decembre 1987

LOW TEMPERATURE ACOUSTIC PROPERTIES OF SILICA AEROGELS

J. BON, E. BONJOUR, R. CALEMCZUK a n d B. SALCE

CEN de Grenoble, DRFG/SBT/Laboratoire de Cryophysique, BP 85 X , F-38041 Grenoble Cedex, France

ABSTRACT :

Low frequency e l a s t i c modulus and acoustic attenuation of s i l i c a aerogel have been measured by t h e resonant bar method.

Measurements were performed on low density samples (d = 0.27 and 0.87 g c m - 3 ) i n the 100 mK

-

^{70 K} temperature range.

The experimental investigation of l o w density s i l i c a aerogels ( p

<

0.8 g ₎ has gained considerable i n t e r e s t i n the l a s t few years [1][2][3]. It is usually believed t h a t these compounds may possess f r a c t a l s t r u c t u r e s since the density of an i d e a l f r a c t a l system approaches zero as the s i z e of the sample increases.

w

These systems a r e successfully described i n terms of f r a c t a l

(i)

and spectral ( d ) dimensions which d i f f e r s i g n i f i c a n t l y f r o m the r e a l space dimension (d) [4].

Alexander e t a l . [5] have used t h i s approach t o analyse the thermal properties of vitreous s o l i d s f o r temperatures above 1 K. The plateau observed between 5 K and 10 K i n the thermal conductivity of such s o l i d s would r e s u l t from the existence of localized harmonic vibration modes (fractons) i n r e l a t i o n t o the f r a c t a l

r"

s t r u c t u r e and would indicate t h a t the density of s t a t e s v a r i e s a s od-l. Below 1 K thermal and acoustical properties of glasses suggest the existence of propagating harmonic excitations (long wavelength phonons) which i n t e r a c t with anharmonic excitations assumed to be two l e v e l systems (TLS) and described with the tunnel- l i n g model.

I n a recent work on s i l i c a aerogels, Calemczuk e t a l . [6] have analysed sound velocity v ( p ) , thermal conductivity K(T) and s p e c i f i c heat C(T) measurements within the f r a c t a l model. A t T below 1 K , the observed behavior f o r C(T) or TQ led

w

to the determination of d = or = 1.1, assuming t h a t C(T) is largely dominated by harmonic excitations. However, the TLS contribution t o C(T) cannot be excluded and the previous analysis would be inappropriate i f the TLS s p e c t r a l density hap- pens t o be an order of magnitude higher than the one observed i n vitreous s i l i c a . It w a s therefore e s s e n t i a l to perform more d i r e c t measurements on TLS i n s i l i c a aerogels. Since acoustical measurements have proven t o be a si l e mean$ f o r

T v

achieving t h i s goal we have measured sound velocity variations

-

(T) and inter- v

nal f r i c t i o n Q-I (TI.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987875

C8-484 JOURNAL DE PHYSIQUE

BASIC CONCEPTS ON ACOUSTIC PROPERTIES

I n t h e t u n n e l l i n g model, t h e TLS a r e well described by a c o n s t a n t s p e c t r a l den-

-

s i t y

P

and can i n t e r a c t with phonons of energy W v i a two d i f f e r e n t mechanisms : a resonant one and a r e l a x a t i o n a l one, both described by a coupling c o n s t a n t

r.

A t a given temperature t h e r e l a x a t i o n times T c h a r a c t e r i z i n g those processes a r e n o t t h e same f o r a l l TLS and a r e bounded by lower c u t - o f f -rm,,. A t very low tem- p e r a t u r e and i n t h e l i m i t where Fid << KT, two l i m i t i n g regimes can be d i s t i n - guished [7] :

P r 2 -

where C =

-

and To is an a r b i t r a r y r e f e r e n c e temperature.

d

For i n s t a n c e , f o r S u p r a s i l W s i l i c a ( p = 2.2 g cmb3) t h e cross-over w . r m i n

=

1 occurs around 200 mK. I n t e r n a l f r i c t i o n p l a t e a u observed between 200 mK and 6 K y i e l d s C

"

2.5 x while t h e Av

-

d a t a l e a d s t o a v a l u e f o r C o f about

v

3.9 x On t h e o t h e r hand, we observe a r e l a x a t i o n peak o f 10-3 n e a r T = 15 K which would n o t be d i r e c t l y l i n k e d to t h e TLS [8].

EXPERIMENTAL METHOD

The samples were prepared a t CEN-Saclay by h y d r o l y s i s o f tetramethoxysilane d i s - solved i n methanol and by removing t h e s o l v a n t i n h y p e r c r i t i c a l c o n d i t i o n s . Small b a r s (30 x 5 x 2 arm3) were c u t o u t of those samples and polished i n o u r labora- t o r y . I n t h e p r e s e n t study t h e samples o r i g i n a t e from t h e same batch as t h e samples used by Calemczuk e t a l . [6] and we s h a l l t h e r e f o r e use t h e same l a b e l - l i n g , namely a (P = 0.87 g cm-3) and c (p = 0.27 g

The measurements have been performed i n a He3/He4 d i l u t i o n c r y o s t a t f o r tempera- t u r e s between 50 mK and 35 K. Below 30 K, t h e samples have been cooled down with no exchange gaz i n o r d e r t o avoid t h e a d s o r p t i o n of helium a t lower temperature.

The resonant bar method has been employed t o measure Q'' and Av

-

as described i n

[9]

^and

[lo].

A l l measurements were done a t the b a r resonance frequency, with the v a i d of a resonance tracking program. An absolute measurement of i n t e r n a l f r i c t i o n is done with the method of cut-off frequency a t one temperature and is used a s a reference, and t h e Q- values a t the o t h e r temperatures a r e deduced from a compa- r i s o n of the o s c i l l a t i o n amplitudes. The r e l a t i v e v a r i a t i o n s of t h e sound velo- c i t y a r e d i r e c t l y r e l a t e d t o the r e l a t i v e v a r i a t i o n of the resonance frequency.

RESULTS AND DISCUSSIONS

The measurement of the bar resonance frequency y i e l d s d i r e c t l y VE -where E is

=

%

Young modulus. We f i n d t h a t the values obtained f o r VE a r e very c l o s e t o the values of the longitudinal v e l o c i t y i n the same samples [6]. This r e s u l t i n d i - c a t e s t h a t t h e Poisson r a t i o is low, i n agreement with what has been observed i n v i t r e o u s s i l i c a [8]. I n f i g u r e 1 we present the r e l a t i v e v a r i a t i o n s of sound velo- c i t y and i n t e r n a l f r i c t i o n measured f o r samples a and c a t frequencies of 3400 Hz and 1000 Hz respectively. We have a l s o shown the r e s u l t s of Raychaudhuri and Hurrklinger [8] ( f u l l curve) f o r a sample of v i t r e o u s s i l i c a S u p r a s i l W a t a f r e - quency of 3170 Hz. The - r e s u l t s Av c l e a r l y show around 70 mK t h e cross-over bet-

v C

ween t h e C LnT regime and the

- -

LnT regime which we have mentioned above. The behavior observed f o r the aerogels is s t r i k i n g l y s i m i l a r t o t h e one observed i n 2 s i l i c a i n t h e high temperature regime. We obtain a

-

h T dependence which extends from 200 m~ to 1 K f o r sample a and from 80 mK t o 0.5 K f o r sample c. Thus, cons- t a n t C is equal to 2.8 x and 3.9 x i n sample a and c respectively. A t higher temperature, the v e l o c i t y decreases much more r a p i d l y i n the neighbourhwd of a r e l a x a t i o n phenomenon a s w i l l be discussed below.

Close analogy can be drawn between the Q-I r e s u l t s f o r t h e aerogels and those f o r t h e s i l i c a . Sample a shows a plateau f o r T lower than 2 K i n agreement with the t h e o r e t i c a l predictions. I n sample c , f o r t h e same temperature range Q-I is seen t o be weakly temperature dependent, even a t the lowest temperature. These r e s u l t s provide an independent determination of C f o r sample a and a lower l i m i t f o r sample c, namely

3

x and 4.9 x respectively.

Above 2 K , Q-I is dominated by a relaxation peak whose i n t e n s i t y maximum I is a t about 16 K. The l a t t e r is l i k e l y t o have the same o r i g i n as the one observed i n t h e s i l i c a although its i n t e n s i t y is much l a r g e r and s l i g h t l y s h i f t e d towards lower temperature.

JOURNAL DE PHYSIQUE

Figure 1 a

-

Relative variation of sound velocity as a function of temperature

+

^{gel a} ; o gel c ;

-

^{Suprasil W}

Figure 1 b

-

Internal friction as a function of temperature + gel a ; o gel c ;

-

^{Suprasil W}

In table 1 we have suarmarized the experimental data f o r sample a and c a s well as those f o r Suprasil W.

Table 1

The calculation of the quantity P y2 from the value of C,

-

p and sound velocity give values 30 times (sample a ) and 1000 times (sample c ) smaller than the one obtained f o r vitreous s i l i c a .

Samplea Sample c SuprasilW

We think t h a t these large differences must be attributed essentially t o varia- tions i n the coupling constant 7. Indeed, 7 is the proportionnality constant bet- ween the variation of the s p l i t t i n g of the TLS and the deformation € a t the macroscopic scale. However, a t the scale of the grains which make up the sample, the macroscopic deformation ends up i n a much weaker deformation E * . Since pV2 represents a mean e l a s t i c constant relating e l a s t i c energy density t o the square of the deformation, we can estimate t h a t , a t l e a s t t o an order of magnitude,

Y V

- - - -

( V and V* correspond to the properties of the grains).

v v*

In t h i s interpretation. our results indicate t h a t i n the different samples the ( g . a i 3

.87 .27 2.2

number of TLS per unit mass is very close t o the one i n vitreous s i l i c a .

However, t h i s analysis based on the application of the TLS model assumes that the l a t t e r i n t e r a c t with delocalized phonons, whose density of s t a t e s

- ^d.

^{We point}

out t h a t , i n the energy range T

>

0.1 K, the thermal measurements 161 have shown t h a t the existing excitations would rather be localized with a density of s t a t e s much smaller than the one predicted by the Debye model (- (3 )

.

REFERENCES

I 2 x 1 0 - 3 1.2 x

8 x 1 0 - ~

c ($1

2 . 8 x 1 0 - ~ 3.9 x 3 . 9 x 1 0 - '

[I] COURTENS E.. PELOUS J., PHALIPPOU J., VACHER R. e t WOIGNIER T..

Phys. Rev. Letters.

58

no 2 (1987). 128

[2] BOUKENTER A., CHAMPAGNON B., DWAL E., DUMAS J.. QUINSON J.F. e t SERUGHETTI J.. Phys. Rev. Letters.

51

no 19 (1986). 2391

[3] SCHAEFER D.W. e t I<EEFER K.D.,

Phys. Rev. Letters. n* 20 (1986). 2199

C ( Q - I )

4.9 x 2 . 5 x 1 0 - ~

"E

( m . s - l ) 3 x 1 0 - ~ 1 . 7 ~ 1 0 3

4.2 x

lo2

5 . 8 x 1 0 3

C8-488 JOURNAL

DE

PHYSIQUE

[4]

RAMMAL R. et TOULOUSE G., J. Physique Lettres,

9 (1983).

L

13 151

ALEXANDER S., LAFZMANS C., ORBACH R. et ROSENBERG H.M..

Phys. Rev. B,

28

no

8 (1983). 4615

[6]

CALEMCZUK R., DE GOER A.M.. SALCE B., MAYNARD R.. et ZAREMBOWITCH A., accepted f o r publication in "Europhysics Letters"

[7]

HUNKLINGER S. et RAYCHAUDHURI A.K., Prog. in Low Temp. Phys.

IX (1986)

181

RAYCHAUDURI A.K. et HUNKLINGER S.. 2. Phys. B,

52 (1984), 113 [9]

JACQMIN L.. These U.S.M. Grenoble

(1984)

[lo]

JACQMIN L., CALEMCZUK R., BONJOUR E. et LOCATELLI M..

J. Phys.

9 (1983),

C

9383